Coulomb’s Law

1 / 77

# Coulomb’s Law - PowerPoint PPT Presentation

Coulomb’s Law. Point Charge :. Line Charge :. Surface Charge :. Volume Charge. Prob. 2.6: Electric Field at a height z above the centre of a circular plate of uniform charge density. (Infinite Sheet). Limiting Case :.

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

## PowerPoint Slideshow about 'Coulomb’s Law' - faustine-gaynor

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

Coulomb’s Law

Point Charge :

Prob. 2.6: Electric Field at a height z above the centre of a circular plate of uniform charge density.

(Infinite Sheet)

Limiting Case :

Prob. 2.41. Electric Field at a height z above the centre of a square plate of uniform charge density.

1. Point charges :

Examples :

1. Point Charge

Applications of Gauss’ Law

Although Gauss’ Law is valid for any kind of charge distribution and any Gaussian Surface, its applicability to determine the electric field is restricted only to symmetrical charge distribution

Prob. 2.16

Long co-axial cable : i) Inner solid cylinder of radius a carrying uniform volume charge density ρ ii) outer cylindrical surface of radius b carrying equal and opposite charge of uniform density σ.

Find field in regions i) s<a ii) a<s<b iii) s>b

Prob. 2.17

Infinite plane slab of thickness 2d (-d<y<d) of uniform volume charge density ρ. Find E in regions i) y<-d ii) –d<y<d iii) y>d

The scalar field is called the electric potential and the point is the zero of the potential

Changing the zero of the potential

Let be the potentials with the zero (reference points) at respectively

Prob. 2.20

One of the following is an impossible electrostatic field. Which one?

For the possible one, find the potential and show that it gives the correct field

Potential of a point charge (zero at infinity) :

Volume Charge :

Prob. 2.26

The conical surface has uniform charge density σ. Find p.d between points a & b

Prob. 2.9

Suppose the electric field in some region is found to be :

a) Find the charge distribution that could produce this field

b) Find the total charge contained in a sphere of radius R centered on the origin. Do it in two different ways.

Work done in moving a charge in an electric field

If the charge is brought from infinity to the point :

Electrostatic Energy of a Charge Distribution

It is the work done to assemble the charge configuration, starting from some initial configuration

Given Config.

Initial Config.

The standard initial configuration is taken to be one in which all small (infinitesimal) pieces of charge are infinitely separated from one another.

The electrostatic energy of a charge distribution can be expressed as an integral over the electric field of the distribution :

A sphere of radius R carries a charge density . Find the energy of the configuration in two different ways.

b) Find the potential everywhere and do the integral :

Prob. 2.45

a) Find the energy by integrating over the field

Prob. 2.33

Find the electrostatic energy of a uniformly charged solid sphere of total charge Q by the following method : Calculate work done in adding charge layer by layer

Electrostatic energy of a point charge Q

Energy of a uniform solid sphere of radius R and total charge Q :

Energy of a point charge Q :

Self and Interaction Energy

are the fields produced by

are the energies of the two charge distributions, existing alone. They are called the self energies of the distributions

is the energy of interaction between them. It is the work done to bring them, already made, from infinity.

2

1

As the two flat faces come infinitesimally close to the charged surface,

Electrostatic Boundary Conditions

Applying Gauss’ law to the pillbox :

2

1

Examples :

1. Infinite Sheet

Conductors

A perfect conductor is a body possessing unlimited supply of charges of each kind (+ve & -ve), at least one of which kind iscompletely free to move within the body and on its surface.

Mathematically a conductor is capable of developing any charge density with the only constraint :

(Neutral Cond.)

-

-

+

+

+

-

+

-

+

-

+

-

+

-

+

-

+

-

+

-

+

-

+

-

-

+

-

+

-

+

-

+

-

+

-

+

-

+

-

-

+

+

Or, since charge can reside only on the surface of a conductor, the only restriction on the surface charge density is :

Properties of a perfect conductor

At equilibrium (After charge flow in the conductor has ceased) :

1. The electric field within the body of the conductor is zero

Otherwise, there is no reason why charge should stop flowing

-

-

+

+

+

-

+

-

+

-

+

-

+

-

+

-

+

-

+

-

+

-

+

-

-

+

-

+

-

+

-

+

-

+

-

+

-

+

-

-

+

+

i) Does the conductor have the necessary ammunition to nullify the external field within?

ii) How long does it take the conductor to nullify the external field?

Gaussian surface S

2. There cannot be any charge density within the body of the conductor

4. The electric field just outside the surface of a conductor is everywhere perpendicular to the surface

Reason : The gradient is everywhere perpendicular the level surface.

5. The electric field at any point just outside the surface of a conductor is related to the surface charge density at that point by :

Reason :

From boundary condition on the field :

Note : The surface of the conductor is everywhere pushed outwards.

Prob. 2.38

A metal sphere of radius R carries a total charge Q. What is the force of repulsion between the two halves of the sphere?

Poisson and Laplace Equation

Combining,

In a charge free region :

Prob. 2.46 : The electric potential of some charge configuration is given by :

Find the charge density and the total charge Q